At present, robotic manipulators are commonly used in manufacturing industry. In many cases, their end-effectors are required to move from one place to the other and follow some desired trajectories. This paper develops a nonlinear backstepping control design scheme with velocity observers for the trajectory tracking control of robotic manipulators. In fact, most of robot manipulator controllers require position as well as velocity measurements to achieve their control objectives, but a lot of robotic systems do not have the velocity measurement devices. Therefore, a velocity observer is designed to estimate the unknown angular velocity of robot manipulators, and then the nonlinear controller based on backstepping design algorithm is developed for the control of robot manipulator systems. The proposed nonlinear backstepping controller is not only to stabilize the robot system, but also to drive the trajectory tracking errors to converge to zero exponentially. Furthermore, some simulation results are given to illustrate the excellent performance of the backstepping control design scheme applied to a two-link robot manipulator.